**Problem 4: Probability Distribution Function (PDF) of a Function of Two Variables**Consider two independent random variables \( x_1 \) and \( x_2 \) that are both uniformly distributed between 9 and 11. The task is to find the probability distribution function (pdf) of the variable \( y_1 \), defined as:\[ y_1 = \frac{x_1 x_2}{x_1 + x_2} \]**Hint:** Introduce the dummy variable \( y_2 = x_2 \) and use the approach of two functions of two variables to solve the problem.This problem requires integrating knowledge of probability theory, specifically, transforming variables to find the pdf of a function involving two random variables.

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Answered: 4. Two independent random variables X₁…

A First Course in Probability (10th Edition)

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Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
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4. Two independent random variables X₁ and x₂ are both uniformly distributed between 9 and 11. Find the pdf of y₁=X1X2/(x₁+x₂). Hint: introduce the dummy variable y2=X2 and use the approach of two functions of two variables.